Is there a math library in Julia which can compute a modified Bessel function of the second kind with complex order and argument? I am only aware of SpecialFunctions.jl which contains a method to compute a modified Bessel function of the second kind with a complex argument of real order.

I had a student working on a related problem at one point — my recollection is that we couldn’t find any free code for this, and very little literature. He developed some prototypes, but as I recall he ran into tricky accuracy issues with the second-kind Bessel functions for complex arguments that were close to integers. We also wanted the derivative with respect to the order, however, so maybe the problem was easier if you don’t need that. I’ll bug him to see whether he has any notes he can post.